Fitting tails affected by truncation
Fitting tails affected by truncation
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DOI：
10.1214/17-ejs1286
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发表时间：
2017-01-01
影响因子：
1.1
通讯作者：
Reynkens, Tom
中科院分区：
文献类型：
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作者：
Beirlant, Jan;Alves, Isabel Fraga;Reynkens, Tom
在一些应用中，最终在最大数据量下，在分析统计分布的尾部特征时可以观察到截断效应。在某些情况下，截断效应是通过地球物理学中的古登堡-里希特关系等物理模型来预测的，而在另一些情况下，测量过程本身的性质可能会导致较大值的恢复，例如，由于河流流量读数中的洪水。最近，Beirlant，Fraga Alves和Gome(2016)讨论了截断Pareto型分布的尾部拟合问题。利用地震分析、水文学和钻石估价的例子，我们论证了对截断的重尾和轻尾进行极值分析的必要性。我们将经典的峰值过阈值方法推广到形状参数为xi&>-1/2的不同最大吸引域，以考虑截断效应。我们使用伪最大似然方法来估计模型参数，并在适当的时候考虑在截断之前的极端分位数估计和分位数水平的重建。我们报告了一些模拟实验，并提供了一些基本的渐近结果。
In several applications, ultimately at the largest data, truncation effects can be observed when analysing tail characteristics of statistical distributions. In some cases truncation effects are forecasted through physical models such as the Gutenberg-Richter relation in geophysics, while at other instances the nature of the measurement process itself may cause under recovery of large values, for instance due to flooding in river discharge readings. Recently, Beirlant, Fraga Alves and Gomes (2016) discussed tail fitting for truncated Pareto-type distributions. Using examples from earthquake analysis, hydrology and diamond valuation we demonstrate the need for a unified treatment of extreme value analysis for truncated heavy and light tails. We generalise the classical Peaks over Threshold approach for the different max-domains of attraction with shape parameter xi > -1/2 to allow for truncation effects. We use a pseudo maximum likelihood approach to estimate the model parameters and consider extreme quantile estimation and reconstruction of quantile levels before truncation whenever appropriate. We report on some simulation experiments and provide some basic asymptotic results.